The amorphous crystalline transition temperature for Si MBE growth is higher for [111] growth than for [100] growth. The mechanism for the growth of amorphous Si in [111] growth is thought to be due to the possibility of of direct formation of stacking faults on the [111] surface. To investigate this mechanism, a kinetic model describing the amorphous-crystalline transition in low temperature Si [111] MBE growth is proposed. The model allows Si atoms to incorporate at three types of sites: A, B and C where A is the triply covalent bonded correct diamond site, B is the triply covalent bonded wrong hep site and C is the singly covalent bonded wrong site. The model allows for the migration of atoms from a wrong site to a nearest neighbor correct site through Arrhenius type rate equations. The migration from B → A is assumed 1000 times weaker than the reverse migration process. Similarly migrations from C → A are assumed 106 time stronger than the reverse migration. All possible migrations are considered with different rates. At the high temperature, the model will allow the growth of a perfect diamond cubic structure with correct ordering of layers AaBbCc etc. A stochastic model describing the above kinetic model is developed based on the master equation approach and random distribution approximation. The low temperature MBE growth of Si [111] is investigated using this model. The results of the model are compared with existing experimental work [1]. The results are in good agreement. The study shows that the kinetics of the site correcting migration process well describes the observed amorphous-crystalline transition in [111] Si MBE growth.